The cost of entering a carnival and riding rides is given by the linear equation, c(r) = 1.25r + 6.00, where c(r) is the total cost of attending the carnival and r is the number of rides. the slope of the linear equation represents the response area .

The value that represents the variable x in the trapezoid is 108 degrees

From the question, the trapezoid represents the given parameter

We can see that the trapezoid is an isosceles triangle

This means that the angle x and y are congruent

The sum of angles is a trapezoid is 360 degrees

So, we have the following summation equation

x + x + 72+ 72 = 360

Evaluate the like terms

So, we have

2x + 144= 360

This gives

2x = 216

Divide by 2

x = 108

Hence, the value of x is 108 degrees

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The true statements about the constraints in this situation are:

In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:

2x + 0.50y = 120

Where:

When x = 40 and y = 60, we have:

2x + 0.50y = 120

2(40) + 0.50(60) = 120

80 + 30 = 120

110 ≠ 120 (Not a solution).

When x = 30 and y = 120, we have:

2x + 0.50y = 120

2(30) + 0.50(120) = 120

60 + 60 = 120

120 = 120 (True solution).

Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.

When x = 0 and y = 240, we have:

2x + 0.50y = 120

2(0) + 0.50(240) = 120

0 + 120 = 120

120 = 120 (True solution).

Therefore, if we buy no beans we can buy 240 pounds of rice.

When x = 0 - 5 and y = 240 + 20, we have:

2x + 0.50y = 120

2(0 - 5) + 0.50(240 + 20) = 120

-10 + 130 = 120

120 = 120 (True solution).

Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.

When x = 0 + 10 and y = 240 - 60, we have:

2x + 0.50y = 120

2(0 + 10) + 0.50(240 - 60) = 120

20 + 90 = 120

110 = 120 (Not a solution).

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As the y-values of a function are the values that the function takes, the largest y-value of a function is called the maximum value of the function

Answer:

30

Step-by-step explanation:

it doesn't seem to be correct question

x=3

the answer is in the photo I took of solving it

486lb of grass seed is required to cover the field on the right.

The area of Rectangle is length times of width

Let us find the areas of two rectangle larger and smaller.

Area of the larger rectangle:

60×90=5400 square feet.

Now divide the larger square area by the smaller square area:

Area of the smaller rectangle

40×50=200 square feet.

Now divide larger rectangle with smaller

5400/200 =27

27 is the ratio of the difference

27×18=486 lb.

Hence 486lb of grass seed is required to cover the field on the right.

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The payment for each 6 h is equal to $ 432.2 while the payment for each 30 min would be  $ 36.01.

It's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.

In the International System Units (SI), the standard unit for time is the second (s).  For solving any exercise, you need to know the relation between the units of the time. See below:

1h=60 min = 3600s

1 min = 60 s

Now you can solve the question from the rule of three for finding the payment in dollars.

The question gives: an each 8.33 min, the payment is 10 dollars. Thus, from this relation you can write:

First, you should convert 6h to minutes, then,

1 h ----- 60 min

6h ----- x

x=60*6=360 min

After that, you should apply the rule of three for finding the payment in dollars.

   8.33 min     -----  10 dollars.

   360 min    -------  x

8.33x=360*10

8.33x=3600

x= $ 432.2

You should apply the rule of three for finding the payment in dollars.

   8.33 min     -----  10 dollars.

   30 min    -------  x

8.33x=30*10

8.33x=300

x= $ 36.01

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Answer:

[tex]\frac{1}{2}[/tex] y +3

Step-by-step explanation:

You want to combine like terms

[tex]\frac{2}{5}[/tex] y and [tex]\frac{-9}{10}[/tex] y are like terms because they both have a variable y

-4 and + 7 are like terms because they are both constants.  (numbers without letters)

We combine these

[tex]\frac{4}{10}[/tex] means the same as [tex]\frac{2}{5}[/tex]  I just multiplied the numerator (top) and the denominator (bottom) by 2.  I did this so that I could add it to [tex]\frac{-9}{10}[/tex]

[tex]\frac{4}{10}[/tex]y - [tex]\frac{9}{10}[/tex]y  = [tex]\frac{-5}{10}[/tex] y (4-9 = -5)  or [tex]\frac{-1}{2}[/tex] y simplified

-4 + 7 = 3

The equation of the required perpendicular line is x + 3y = 24.

What is the slope relation for two perpendicular lines?
For two perpendicular lines on a plane, the product of their slopes always equals (-1).
What is the equation of line with slope 'm' and passing through the point (x₁, y₁)?
The standard equation of the line with slope 'm' and passing through the point (x₁, y₁) is y - y₁ = m(x - x₁).

Given, the required line is perpendicular to line given by y = 3x + 5 with slope, m₁ as 3, on analysis with standard equation of line; also the line passes through the point (9, 5) i.e. (x₁, y₁).
Let the slope of the required line be = m₂
As per statement established in the literature above, we have:
Slope of two perpendicular lines = -1
∴m₁ × m₂ = -1 ⇒ 3m₂ = -1 ⇒ m₂ = (-1)/3
Again, equation of the required perpendicular line is:
y - 5 = [(-1)/3][x - 9] ⇒ 3y - 15 = 9 - x ⇒ x + 3y = 24
Thus, the equation of the required perpendicular line is x + 3y = 24.

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By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.

So, the values in the blank will be:

Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.

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From the information given,

Jack wants to eat 2 1/5 of his plate in 1/3 hour. The first step is to convert 2 1/5 to improper fraction. It becomes 11/5

The statement would be

Jack wants to eat 11/5 of his plate in 1/3 hour.

Let x represent how much of his plate that he will eat in 1 hour. Therefore

11/5 = 1/3

x = 1

By cross multiplying, it becomes

x * 1/3 = 1 * 11/5

x/3 = 11/5

x = 11/5 * 3

x = 33/5

Converting to mixed fraction, it becomes

6 3/5

The correct option is the first one

Answer:

The answer would be 1.3, and the three is repeating.

Step-by-step explanation:

First, make 4 2/15 into a improper fraction.

4 2/15= 62/15

Now, when we divide fraction, use the rule Keep, Change, Flip.

Keep the 62/15.

Change the division sign into a multiplication sign.

To make the 3.1 into a fraction, put a one over it.

3.1/1

Now, flip the fraction.

3.1/1= 1/3.1

Your equation will look like this:

62/15x1/3.1

Multiply across.

62/46.5

Now simplify.

The answer would be 1.3, and the three is repeating.

To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:

Then;

Since we want to find the measure of angle x, we can use:

c = 175 mi

a = 200 mi

b = 50 mi

C = x

Now, by the Law of Cosines:

And solve:

To the nearest whole number, x = 54°

The length of the incline of the ramp will be [h] = 12.0415 ft

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -

h² = p² + b²

Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.

From the data given, we can consider the ramp construction as right angled triangle. We can write -

base [b] = 12 ft

height [p] = 1 ft

Using the Pythagoras theorem -

h² = (12 x 12) + (1 x 1)

h² = 144 + 1

h = √145

h = 12.0415

Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft

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[This question also has part B. Visit the following link for part B -

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[tex]2x = 76[/tex]

Due to alternate angles

[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]

40°+(y-8)°+76°=180°(sum of angles in a triangle)

[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]

ATTACHED IS THE SOLUTION.

Answer:

x = 38 ; y = 72

Step-by-step explanation:

180 = 76 + 40 + (y - 8)

180 = 108 + y

72 = y

The triangle has parallel lines, so the uppermost right angle is also 90 degrees.

90 - 76 = 14

180 = 90 + 14 + 2x

180 = 104 + 2x

76 = 2x

38 = x

Answer:

correct me if im wrong but my answer is x=7, or in other words, 7.

Step-by-step explanation:

Answer:

7 years old

Step-by-step explanation:

You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13

The Answer, 7 years old

Answer:  The slope is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{-8-(-6)}{-2-1} =\frac{-2}{-3} =\frac{2}{3}[/tex]

The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:

Then to find the mass we just multiply the weight in pounds by 0.45:

Therefore the other person has a mass of 45 kg.

The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:

Then to find the mass we just multiply the weight in pounds by 0.45:

Therefore the other person has a mass of 45 kg.

Answer:

-8

Step-by-step explanation:

SOLUTION

Given the question in the question tab, the following are the solution step to get the number of books they have altogether.

Step 1: Write the notations for Joseph's and Mike's books

Step 2: Write the statements in a mathematical form

Step 3: Solve to get the value of j by using substitution method

Therefore, Joseph had 84 books initially.

Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially

Hence, they both had 112 books altogether.

Approximately 34% of people sleep more than 8.5 hours per night.

According to the Empirical Rule states for a normally distributed random variable: 68% of the measures are within 1 standard deviation of the mean, 95% of the measures are within 2 standard deviations of the mean and 99.7% of the measures are within 3 standard deviations of the mean. According to the question, Mean = 7 and Standard deviation = 1.5. Also, in the question the normal distribution is symmetric, which means that 50% of the measures are below the mean and the rest 50% are above the mean. Now, the mean is 7 and 8.5 is 1 one standard deviation above the mean. So, by the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean (more than 8.5 hours). So, we get

0.5*0.68 = 0.34 which is equal to 34%.

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Answer: [tex]x=15[/tex]

Step-by-step explanation:

By the consecutive interior angles theorem,

[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]

The lower value of the perimeter is 140 inches .

Width of the rectangle is 20 inches .

The length of the rectangle is calculated as ,

Rearranging the terms ,

The higher value of perimeter is 220 inches .

Width of the rectangle is 20 inches .

The length is calculated as,

Therefore,

Thus the range of values for the length of the given rectangle are 50 and 90 .

Answer:

12r^3

Step-by-step explanation:

The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]

The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:

V = 2x (x - 1) (x + 2) ≤ 280

Divide both sides by 2:

x (x - 1) (x + 2) ≤ 140

x³ + x² - 2x - 140 ≤ 0

(x - 5) (x² + 6x + 28) ≤ 0

Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:

x - 5  ≤ 0

or x  ≤ 5

Using the interval notation, x = (-∞, 5]

However, remember that the dimension is always a positive number.

Hence,

x - 1 ≥ 0

or x  ≥ 1

Therefore, the solution is [1, 5]

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Step 1: redraw the figure given

Step 2: State the relationship between the lines

It can be observed that

(i) line XY is perpendicular to line PS

(ii) line XY is perpendicular to line QT

(iii) line PS is parallel to line QT

Hence, XY⊥PS, XY ⊥ QT, PS ║ QT, The Second option.

The vertex of a parabola is the extreme point (maximum or minimum, depending on the the sign of the quadratic coefficient).

In the graph, we can see that the x-coordinate of the vertex is x=-1 and the y-coordinate is y=3.

Then, we can write the coordinates of the vertex as (h,k) = (-1,3)

Answer: The coordinates of the vertex are (-1,3)

The image of triangles are given .

a.

b. Find the ratio,

c.Hence the triangles are similar .

The correct option is A.